Page 77 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 57

Figure 2.10 Position vector R of the earth relative to the IJK
frame.

Care also must be taken regarding the sign conventions used for lati-
tude and longitude because different systems are sometimes used, depend-
ing on the application. In this book, north latitudes will be taken as positive
numbers and south latitudes as negative numbers, zero latitude, of course,
being the equator. Longitudes east of the Greenwich meridian will be
taken as positive numbers, and longitudes west, as negative numbers.
The position vector of the earth station relative to the IJK frame is R as
shown in Fig. 2.10. The angle between R and the equatorial plane, denoted
by y in Fig. 2.10, is closely related, but not quite equal to, the earth sta-
E
tion latitude. More will be said about this angle shortly. R is obviously a
function of the rotation of the earth, and so first it is necessary to find the
position of the Greenwich meridian relative to the I axis as a function of
time. The angular distance from the I axis to the Greenwich meridian is
measured directly as Greenwich sidereal time (GST), also known as the
Greenwich hour angle, or GHA. Sidereal time is described in Sec. 2.9.4.
GST may be found using values tabulated in some almanacs (see
Bate et al., 1971), or it may be calculated using formulas given in Wertz
(1984). In general, sidereal time may be measured in time units of side-
real days, hours, minutes, seconds, or it may be measured in angular
units (degrees, minutes, seconds, or radians). Conversion is easily
accomplished, since 2p radians or 360° correspond to 24 sidereal hours.
The formula for GST in degrees is
2
GST 99.9610° 36000.7689° T 0.0004° T UT° (2.34)